Time of flight calibration in digital positron emission tomography

ABSTRACT

Time of flight (TOF) corrections for radiation detector elements of a TOF positron emission tomography (TOF PET) scanner are generated by solving an over-determined set of equations defined by calibration data acquired by the TOF PET scanner from a point source located at an isocenter of the TOF PET scanner, suitably represented as matrix equation Formula I=CS where Formula I represents TOF time differences, C is a relational matrix encoding the radiation detector elements, and S represents the TOF corrections. A pseudo-inverse C −1  of relational matrix C may be computed to solve S=C −1  Formula I. TOF corrections can be generated for a particular type of detector unit by identifying the radiation detector elements in C by detector unit. Further, multi-photon triggering time stamps can be adjusted to first-photon triggering based on Formula II where P1 is average photon count using first-photon triggering and Pm is a photon count using multi-photon triggering.

The following relates generally to positron emission tomography (PET)arts, including time-of-flight (TOF) PET, and to medical imaging usingPET, a gamma camera, or another radioemission-based imaging technique,and the like; and to radiation detector time-stamping circuitry arts,radiation detection event time-stamping arts, and related arts.

In positron emission tomography (PET) medical imaging, aradiopharmaceutical is administered to a subject to be imaged. Theradiopharmaceutical includes positron-emitting radioisotopes, and thepositrons combine with electrons in positron-electron annihilationevents each of which emits two oppositely directed 511 keV gamma rays(also called gamma particles, these terms being used interchangeablyherein). The PET scanner includes radiation detectors disposed aroundthe subject, usually forming an encircling ring of radiation detectors.Energy and time windowing are applied to the detected radiation eventsto identify coincident (or nearly coincident, i.e. within TOF of thegamma rays from the location of the positron-electron annihilation eventto the respective detectors) 511 keV radiation detection events.

In conventional PET, each such 511 keV gamma ray pair defines a “line ofresponse” between the detection events at the respective detectors, andthe positron-electron annihilation event is known to be localized alongthat line. This localization is sufficient to reconstruct an image ofthe radiopharmaceutical distribution in the subject using a suitablereconstruction technique such as filtered backprojection, iterativeforward-backward projection, various Fourier transform imagereconstruction techniques, or so forth.

In time-of-flight (TOF) PET, a further resolution improvement isobtained by determining a localization of the positron-electronannihilation event along the line-of-response based on the difference(if any) between the constituent 511 keV detection events. For example,if both 511 keV detection events occurred at precisely the same time,then the positron-electron annihilation event was located equidistantbetween the two detectors. On the other hand, if detector “A” detectedits 511 keV event at some time before detector “B”, then thepositron-electron annihilation event was located closer to detector “A”versus detector “B”, and the quantitative time difference enablesquantitative positioning of the event along the line of response.

TOF resolution, accuracy, and precision depend on the accuracy of the(difference in) time stamps assigned to the 511 keV detection events ofa coincident pair. Due to the high speed of light (approximately 3×10¹⁰cm/s, or 0.03 cm/picosecond), time stamp accuracy on the order of a fewtens of picoseconds or better is preferable in order to provide usefulTOF localization along the line of response. This is difficult toachieve across an encircling array of detectors that is large enough toreceive a medical subject. Temporal variations can occur at the detectorelement or crystal level (that is, at the scintillator level in the caseof radiation detectors comprising scintillator crystals with coupledoptical detectors) due to differences in detector response times, or ata higher level (e.g., module level) due to differences in electricalsignal propagation times or other factors.

In the case of radiation detectors that employ scintillators, anotherdifficulty in obtaining precise time stamping resides in the cascadenature of the scintillation event. When a gamma ray is absorbed by thescintillator crystal, a burst of light (scintillation) is generated thatextends over time and has some finite photon emission-versus-timeprofile which is read by a photomultiplier tube (PMT),semiconductor-based photodetector, or other light detector as photoncounts over the time of the scintillation burst. The trigger for timestamping must be defined with respect to this distribution. Varioustriggers can be used, such as triggering the time stamp on receipt thefirst photon (1^(st) photon trigger), or triggering the time stamp onreceipt within a time window of two (or more) photons (multi-photontrigger). Since TOF accuracy depends on relative time stamps of 511 keVdetection pairs, in principle any trigger could be used so long as it isuniformly applied across the detectors. In practice, 1^(st) photontriggering provides the best temporal resolution, but at the cost ofhigher noise since detector dark current can be more easily mistaken fora scintillation trigger. Multi-photon triggering is less noisy but alsoprovides poorer resolution.

The present application provides a new and improved system and methodwhich overcome these problems and others.

In accordance with one aspect, a time-of-flight positron emissiontomography (TOF PET) imaging system is disclosed, including a TOF PETscanner comprising radiation detector elements and an electronic dataprocessing device programmed to: operate the TOF PET scanner to acquirecalibration data comprising annihilation event data acquired forpositron-electron annihilation events occurring in a point sourcelocated at an isocenter of the TOF PET scanner wherein each annihilationevent datum includes an identification of the radiation detectorelements detecting two oppositely directed 511 keV gamma rays emitted bythe annihilation event and a time difference between detection of thetwo oppositely directed 511 keV gamma rays emitted by the annihilationevent; generate TOF corrections for the radiation detector elements bysolving an over-determined set of equations defined by the calibrationdata; operate the TOF PET scanner to acquire list mode imaging datacomprising 511 keV gamma ray detection events acquired from an imagingsubject; generate corrected list mode imaging data by applying the TOFcorrections to the list mode imaging data; and reconstruct the correctedlist mode imaging data to generate a reconstructed image of at least aportion of the imaging subject. The TOF corrections may be generated bysolving the matrix equation Δt=CS for S, where Δt stores the timedifferences of the calibration data, C is a relational matrix encodingthe identifications of the radiation detector elements, and S stores theTOF corrections. This matrix equation may, for example, be solved bycomputing a pseudo-inverse C⁻¹ of the relational matrix C and computingS=C⁻¹ Δt.

In accordance with another aspect, in a TOF PET imaging system as setforth in the immediately preceding paragraph and in which the TOF PETscanner is operated to acquire list mode imaging data using multi-photontriggering, the electronic data processing device may be furtherprogrammed to adjust time-stamps of the list mode imaging data to valuesthat would have been obtained using first-photon triggering. In oneapproach, time-stamps TS_(m) of the list mode imaging data acquiredusing multi-photon triggering are adjusted to estimated first-photontriggered time stamps

${TS}_{1} = {{TS}_{m} - {a\sqrt{\frac{b}{Pm}}}}$

where a and b are constants and Pm is the photon count for a list modeimaging datum acquired using multi-photon triggering.

In accordance with another aspect, a non-transitory storage mediumstores instructions readable and executable by an electronic dataprocessing device to perform a method operating on radiation detectionevent data acquired using a radiation detector element comprising ascintillator and a light detector coupled with the scintillator. Themethod suitably comprises: determining an average photon count P1 forthe radiation detector element operating with first photon triggeringbased on calibration data acquired by the radiation detector elementusing first-photon triggering; determining a photon count Pm for animaging radiation detection event detected by the radiation detectorelement during imaging of a subject using multi-photon triggering; andestimating a first-photon triggered time-stamp for the imaging radiationdetection event based on the value √{square root over (P1/Pm)}. In someembodiments the average photon count P1 for the radiation detectorelement operating with first photon triggering is determined by fittinga Gaussian distribution to a photon count per event histogram acquiredby the radiation detector element using first-photon triggering.

In accordance with another aspect, a method comprises generating TOFcorrections for radiation detector elements of a TOF PET scanner bysolving an over-determined set of equations defined by calibration dataacquired by the TOF PET scanner from a point source located at anisocenter of the TOF PET scanner, and correcting time stamps of imagingdata acquired by the TOF PET scanner from an imaging subject using thegenerated TOF corrections. These operations are suitably performed by anelectronic data processing device. In one approach, the TOF correctionsare generated from calibration data comprising 511 keV gamma raydetection events each associated with a radiation detector element ofthe TOF PET scanner by operations including: performing time windowingon the 511 keV gamma ray detection events to identify 511 keV gamma raydetection event pairs corresponding to positron-electron annihilationevents; and solving the over-determined set of equationsΔt_(d)=s_(i)+s_(j) where d indexes the d^(th) 511 keV gamma raydetection event pair, i and j index the two radiation detector elementsthat detected the d^(th) 511 keV gamma ray detection event pair, Δt_(d)denotes the time difference between the gamma ray detections of the 511keV gamma ray detection event pair, s_(i) denotes the TOF correction forthe i^(th) radiation detector element, and s_(j) denotes the TOFcorrection for the j^(th) radiation detector element. The TOFcorrections can be generated for a particular type of detector unit bygrouping the calibration data by detector unit based on detector unitdefinitions that assign radiation detector elements of the TOF PETscanner to detector units, and solving the over-determined set ofequations defined by the calibration data with the radiation detectorelements identified in the calibration data by detector unit based onthe grouping. The detector unit definitions may assign radiationdetector elements of the TOF PET scanner to detector modules, detectortiles within detector modules, or scintillator crystals within detectortiles, and the grouping and solving may be repeated for detectormodules, detector tiles, and scintillator crystals in succession witheach successive repetition acting on the calibration data corrected bythe TOF corrections generated by the previous repetition. The methodoptionally further includes adjusting a time stamp of a 511 keV gammaray detection event of the imaging data acquired by a radiation detectorelement using multi-photon triggering to an adjusted time stampcorresponding to first-photon triggering based on the value √{squareroot over (P1/Pm)} where P1 is an average 511 keV gamma ray detectionphoton count for the radiation detector element using first-photontriggering and Pm is the photon count of the 511 keV gamma ray detectionevent of the imaging data.

One advantage resides in improved temporal resolution in time stampingcircuitry of radiation detectors.

Another advantage resides in improved TOF PET image quality as aconsequence of improved TOF resolution.

Another advantage resides in faster TOF calibration of a TOF PET system.

Still further advantages of the present invention will be appreciated tothose of ordinary skill in the art upon reading and understand thefollowing detailed description.

The invention may take form in various components and arrangements ofcomponents, and in various steps and arrangements of steps. The drawingsare only for purposes of illustrating the preferred embodiments and arenot to be construed as limiting the invention.

FIG. 1 diagrammatically shows a digital time of flight positron emissiontomography (digital TOF PET) imaging system including TOF calibrationand event time stamping aspects.

FIG. 2 diagrammatically shows operation of the 1^(st) photon triggerestimator module of the TOF PET system of FIG. 1.

FIG. 3 plots an energy spectrum obtained using 1^(st) photon triggering,along with a Gaussian fitted to the peak.

FIG. 4 diagrammatically shows operation of the TOF calibration module ofthe TOF PET system of FIG. 1.

FIG. 5 diagrammatically shows a matrix formulation of the TOFcalibration optimization performed by the TOF calibration module of FIG.4.

FIG. 6 diagrammatically shows a suitable process for generating TOFcorrections at the module, tile, and crystal level.

With reference to FIG. 1, a time of flight positron emission tomography(TOF PET) scanner 10 includes a scanner housing 12 supporting radiationdetectors 14 arranged as a ring around an examination region. Forimaging of human subjects, the examination region is suitably ahorizontal bore sized to receive a prone human subject. A subjectsupport 16 is arranged to enable a human subject to be loaded into theexamination region in a horizontal position. The TOF PET scanner 10 may,by way of illustrative example, be a Vereos digital PET/CT scanner(available from Koninklijke Philips N.V., Eindhoven, The Netherlands)which also includes transmission computed tomography (CT) scanningcapability not described herein. The radiation detectors 14 areconfigured to detect 511 keV radiation and may, by way of illustrativeexample (see inset at upper left of FIG. 1), employ scintillatorcrystals 20 coupled with optical detectors 22 such as digital siliconphotomultiplier (SiPM) arrays, analog avalanche photodiode arrays,photomultiplier tube (PMT) detectors, or so forth. In illustrative FIG.1 the radiation detectors 14 are diagrammatically indicated—in a typicalcommercial TOF-PET scanner the radiation detectors are covered by a boreliner or otherwise disposed inside the scanner housing and are notexternally visible.

In operation, a subject is administered a radiopharmaceutical thatincludes a positron-emitting radioisotope. The radiopharmaceutical maybe designed to aggregate in an organ or tissue of interest, such as thebrain, lungs, a tumor, or so forth. The subject is loaded into theexamination region via the subject support 16, and the radiationdetectors 14 are operated to detect 511 keV gamma rays. To this end, aradiation particle is absorbed by the scintillator crystal 20 of aradiation detector 14 which generates a burst of light (scintillation)in the scintillator crystal 20. The scintillation comprises a burst ofphotons which are detected by one or more optical detectors 22 of theradiation detector. The radiation detector includes energy integrationcircuitry (for example, employing photon counting) to estimate theparticle energy and time stamping circuitry that generates at time stampfor the radiation detection event. The estimated energy is preferablywindowed to eliminate detection events not corresponding to 511 keVgamma rays. To this end, the radiation detectors 14 preferably includeon-board digital processing capability to generate the time stamp andenergy estimation as digital values. The resulting event data areoffloaded to an electronic data processing device, e.g. computer 24 andare stored in data storage 26, preferably as list mode data storing thetime stamp and energy of each event along with detector information.

The time stamp information of the list mode data generated by the TOFPET scanner 10 may have errors due to differences in response speedamongst the scintillator crystals and/or optical detectors, due todifferences in electronic signal processing propagation speed amongstradiation detector modules, or so forth. To compensate for this, theelectronic data processing device 24 is programmed to implement a timecorrection module 30 that applies a TOF calibration (to be described) tothe radiation detector-generated time stamps. A 511 keV pair detector 32examines the list mode data (preferably with the time correctionperformed by the module 30) to identify coincident 511 keV pairs. Tothis end, the 511 keV pair detector 32 suitably applies a time window tothe list mode events data to detect event pairs that occurred within asmall time window corresponding to the maximum possible difference inTOF travel time for oppositely directed 511 keV gamma rays emitted by asame positron-electron annihilation event. The 511 keV pair detector 32may also utilize other information in filtering the list mode data toidentify 511 keV pairs corresponding to positron-electron annihilationevents—for example, since the two gamma rays emitted by apositron-electron annihilation event travel in opposite directions, twotemporally coincident 511 keV detection events on the same detectormodule cannot have been generated by a positron-electron annihilationevent in the examination region. A TOF localization module 34 processesthe identified coincident 511 keV detection pairs to determine TOFlocalization information along the line of response connecting the twodetection events, so as to generate TOF PET data that is reconstructedby an image reconstruction module 36 using a suitable reconstructionalgorithm (such as filtered backprojection, iterative forward-backwardprojection, various Fourier transform image reconstruction techniques,or so forth) to generate a reconstructed image of the subject (or of amore limited field of view of the subject). The reconstructed image isutilized by an image processing/display module 38, for example toperform medically useful diagnostic, monitoring, or other analysis.

In the foregoing imaging data acquisition, pre-processing, andreconstruction, the time correction module 30 applies TOF calibrationcorrections that were generated prior to the subject imaging session. Inapproaches disclosed herein, the TOF calibration corrections aregenerated based on calibration data acquired by the TOF PET scanner 10for a point source 40 that (during the calibration process) is loaded atan isocenter of the TOF PET scanner 10. The isocenter of the TOF PETscanner 10 is defined as follows: For any positron-electron annihilationevent occurring at the isocenter, the two oppositely directed gamma raysgenerated by the annihilation event have equal (ground-truth) TOF traveltimes to their respective radiation detectors. Said another way, the twogamma rays of the gamma ray pair detected for any positron-electronannihilation event at the isocenter of the TOF PET scanner 10 should bedetected at precisely the same time. The actual time stamps assigned bythe radiation detectors 14 for the two gamma ray detection events may,however, be different, due to differences in detector response times,differences in signal propagation in the detector electronics, or soforth. During imaging data acquisition, the time correction module 30applies TOF calibration corrections to compensate for these effects.

With continuing reference to FIG. 1, the point source 40 located at theisocenter of the TOF PET scanner 10 during calibration may, for example,be a Na-22 point source. More generally, the point source 40 is a smallelement whose compactness is sufficient that all positron-electronannihilation events occurring anywhere in the point source 40 can beconsidered to have occurred at the isocenter of the TOF PET scanner 10.For example, in some embodiments the disclosed TOF calibrationtechniques enable TOF resolution of below 300 picoseconds to beobtained. Light traveling at 0.03 cm/ps travels 9 cm in 300 picoseconds,so for this example the point source 40 should be less than 9 cm in size(e.g. diameter), and more preferably less than 5 cm in size, and stillmore preferably less than 1 cm in size.

In the illustrative system of FIG. 1, two timing adjustments aregenerated during the TOF calibration. One adjusts a time stamp generatedusing a multi-photon time stamp trigger to a time stamp that would havebeen generated using a single-photon time stamp trigger. This adjustmentis performed by a 1^(st) photon trigger estimator module 42 which isdescribed in further detail herein, and generates 1^(st) photon triggerconversion parameters 44 that are henceforth applied to acquired subjectimaging data by the time correction module 30. This adjustment isoptional, but if used advantageously enables time stamps for list modeimaging data to be generated in response to a multi-photon (e.g.two-photon) trigger so as to reduce the impact of noise, while at leastpartially recovering the better time resolution that would have beenobtained by time stamping in response to 1^(st) photon triggering.

The second timing adjustment is a TOF correction that accounts forvariations in detector response time and for variations in signalpropagation amongst different detector units, and is performed by a TOFcalibration module 50 which is described in further detail herein. TheTOF calibration module 50 advantageously operates on data acquired fromthe point source 40 in a single acquisition session, and this acquiredcalibration data can be reprocessed using different detector unitgroupings to generate TOF corrections for different detector units. Inthe illustrative example, the radiation detectors 14 are assumed to beconstructed as a set of detector modules, and there is a TOF correctionfor each detector module that corrects for signal propagation delay orother factors associated with the module. To this end, moduledefinitions 52 identify the radiation detector elements associated witheach module. In one illustrative example, there are 18 modules, althoughmore or fewer modules are contemplated. Within each detector module, theradiation detector elements are physically laid out on a set of tiles(e.g. circuit boards, or silicon wafers in the case of monolithic SiPMarrays, or so forth). In one illustrative example, each module includes20 such tiles, so that the entire detector ring has 20×18=360 tiles,with the radiation detectors of each tile identified by tile definitions54. In embodiments in which scintillator crystals are employed, anotherTOF correction may be associated with each scintillator crystal, asdifferent scintillator crystals may have different response times.Crystal definitions 56 identify the groupings of radiation detectors bycrystal. In general, each detector tile includes one or morescintillator crystals. These are merely illustrative examples, and otherdetector unit types may be usefully defined based on factors such as thephysical layout and construction of the radiation detector ring.

The TOF PET imaging system of FIG. 1 is an illustrative example, andnumerous variants are contemplated. For example, in one variant theradiation detectors 14 are analog devices, and analog signals (e.g.pulses corresponding to photon counts generated by the optical detectors22) are offloaded to the computer 24 which then generates the energyestimate and the initial time stamp that is then modified by operationof the time correction module 30. More generally, the data processingoperations may be variously allocated between on-board electronics ofthe TOF PET scanner 10 and off-board electronic data processingdevice(s) such as the computer 24, or cloud computing resources, or soforth, and this is diagrammatically represented in FIG. 1 by a genericelectronic data processing device 60 representing the combinedprocessing hardware of the TOF PET scanner 10 and off-board electronicdata processing device(s) 24 some of which may be cloud-based.

It will be further appreciated that the TOF PET calibration and imagingdata processing techniques disclosed herein may be embodied by anon-transitory storage medium storing instructions readable andexecutable by the electronic data processing device 60 to perform thedisclosed techniques. Such a non-transitory storage medium may comprisea hard drive or other magnetic storage medium, an optical disk or otheroptical storage medium, a cloud-based storage medium such as a RAID diskarray, flash memory or other non-volatile electronic storage medium, orso forth.

With continuing reference to FIG. 1 and with further reference to FIGS.2 and 3, an illustrative embodiment of the 1^(st) photon triggerestimator module 42 is described. This timing adjustment estimates thetime stamp that would be obtained in response to a 1^(st) photon triggerbased on the time stamp actually obtained using a multi-photon (e.g.two-photon) trigger. The resulting adjusted time stamp has improvedresolution as expected for 1^(st) photon triggering, but without theconcomitant increased noise associated with triggering on the firstphoton received from a scintillation burst. With reference to FIG. 2, ina first operation 70, energy spectra are acquired for each radiationdetector element using 1^(st) photon triggering. FIG. 3 plots such anenergy spectrum S, with the photon counts per event on the abscissa andthe number of total events having that photon count on the ordinate. Inan operation 72 indicated in FIG. 2, a photon count centroid, denotedherein as P1, is determined for each detector element. In theillustrative embodiment, operation 72 is performed using a Gaussian fitaccording to:

$\begin{matrix}{G = {a_{0} + {a_{1}e^{\frac{- {({x - \mu})}^{2}}{\sigma^{2}}}}}} & (1)\end{matrix}$

where α₁ and α₂ are linear constants, x is the abscissa parameter, μ isthe fitted centroid (or mean), and σ² is the fitted variance. Theparameters α₀, α₁, μ, and σ² are fitted, and the output of operation 72is the fitted centroid P1_(cal)=μ. In FIG. 3 the fitted Gaussian G isalso plotted, with the fitted calibration centroid P1_(cal) indicated bya vertical line. It will be recognized that the centroid P1_(cal)denotes the most likely photon count for the radiation detector elementwhen the event detection is triggered using 1^(st) photon triggering.More generally, it is contemplated to employ other distributions, and/orfitting expressions, for determining the photon count centroid (ormean).

With continuing reference to FIG. 2, in an operation 74 energy spectraare acquired for each radiation detector element using the multi-photon(e.g. two photon) triggering that will be used during imaging dataacquisition. Equation (1) (or another suitable centroid or meanfunction) is applied to this spectrum as well, yielding a centroid Pm=μfor the multi-photon triggering. The TOF adjustment Δt_(m→1) to estimatethe time stamp TS₁ for 1^(st) photon triggering from the time stampTS_(m) actually measured using multi-photon triggering is then given (inthe illustrative case employing Equation (1) as the centroid function)by:

$\begin{matrix}{{\Delta \; t_{m\rightarrow 1}} = {k\sqrt{\frac{P\; 1}{Pm}}}} & (2)\end{matrix}$

If another centroid function is employed, Equation (2) is suitablyadjusted accordingly. A calibration value k_(cal) for the constant k isdetermined empirically in an operation 76 by fitting the time stamps TS₁and TS_(m) for the calibration data acquired in operations 70, 74respectively. The TOF adjustment Δt_(m→1) for a list mode imaging datumis then applied to approximate first-photon triggering as follows:

$\begin{matrix}{{TS}_{1} = {{{TS}_{m} - {\Delta \; t_{m\rightarrow 1}}} = {{TS}_{m} - {k_{cal}\sqrt{\frac{P\; 1_{cal}}{Pm}}}}}} & (3)\end{matrix}$

where the right-most expression is for the illustrative exampleemploying Equations (1) and (2). To generalize, for a given list modeevent acquired as part of the imaging data using the multi-photontriggering, the time stamp using 1^(st) photon triggering is estimatedby: (i) obtaining the actual photon count Pm for the imaging data eventacquired using the multi-photon triggering (this is, or corresponds to,the energy estimate part of the list mode datum); and (ii) applyExpression (3) (or an equivalent) using this Pm and using thecalibration values P1_(cal) and k_(cal) generated in operation 72 andoperation 76, respectively.

The TOF adjustment of Equation (3) is optional. If applied, itadvantageously provides improved resolution comparable with 1^(st)photon triggering without concomitant increased noise. However, in othercontemplated embodiments this TOF adjustment is omitted, and themeasured time stamps TS_(m) are used without this adjustment.

With returning reference to FIG. 1, a suitable process performed by theTOF calibration module 50 entails acquiring a coincidence data set froma point source at the isocenter, measuring the difference in 511 keVdetection time stamps of opposing detectors to get the TOF difference,distributing this difference to these detectors' clocks, and iterativelyrepeating the process until convergence is reached. This approach isslow as the process must be iterated until each detector element issampled sufficiently, which can take well over an hour with existing TOFPET scanner systems. The explicit distribution nature of the approachalso calls for the use of a scatter cylinder and masks the strongestsignal off. Using scattered events that do not come from the isocenter,and noisier data due to the masked peak, reduces the calibrationaccuracy. The iterative nature of the calibration also requires multipledata acquisitions. Additionally, if calibrations are to be performed atdifferent hardware levels (e.g. crystal, tile, module) then theiterative process including iterative data acquisitions must be repeatedfor each level.

With continuing reference to FIG. 1 and with further reference to FIGS.4 and 5, disclosed herein is an improved TOF calibration approachsuitably implemented by the TOF calibration module 50, which operates ona single data set from the point source 40 and can re-process the dataset multiple times to generate a calibration for each detector unit(e.g., module, tile, crystal) of interest. With reference to FIG. 4, inan operation 80 list mode calibration data are collected using the TOFPET scanner 10 with the point source 40 located at the isocenter. In anoperation 82, the list mode data generated in operation 80 are processedby the 511 keV pair detector 32 (see FIG. 1, processing here donewithout applying the time correction module 30) to generate a data setfor positron-electron annihilation events each having a TOF differenceΔt. Without loss of generality, these positron-electron annihilationevents are indexed as d=1, . . . , M where M is the number ofpositron-electron annihilation events in the data set. To illustrate,the d^(th) positron-electron annihilation event is represented by threevalues: first and second detector element identifier values e_(d,i) ande_(d,j) identifying the respective detector elements that detected thetwo oppositely directed 511 keV gamma rays of the d^(th)positron-electron annihilation event); and a TOF offset Δt_(d) (which isin general a signed value to indicate which detector element e_(d,i) ore_(d,j) detected its event first). In an operation 84 thepositron-electron annihilation events are grouped respective to detectorunit of interest (e.g. by module based on the module definitions 52, orby tile based on the tile definitions 54, or by crystal based on thecrystal definitions 56, see FIG. 1). In effect, this transforms thedetector element identifier values e_(d,i) and e_(d,j) to detector unitidentifiers p_(d,i) and p_(d,j) where (using modules as the unit ofinterest in this example) p_(d,i) identifies the detector module towhich detector element e_(d,i) belongs, and p_(d,j) identifies thedetector module to which detector element e_(d,j) belongs.

The resulting information can be represented by a vector of timedifferences 86 denoted herein as Δt of length M, and by a relationalmatrix 88 denoted herein as C that encodes the detector unit informationp_(d,i) and p_(d,j). For example, in one suitable formalism therelational matrix C is a binary matrix of dimensions M×N whose d^(th)row has all 0 values except for having 1 values in the i^(th) and j^(th)columns to encode the two detector units p_(d,i) and p_(d,j) involved indetecting the d^(th) positron-electron annihilation event. In thisnotation, the M rows correspond to the M positron-electron decay events,and the N columns correspond to N units of interest (e.g. N modules, orN tiles, or N crystals, depending upon the unit of interest).

With this matrix formalism in place, in an operation 90 the TOFcalibration is determined by solving the matrix equation:

Δ t=CS  (4)

for the skew vector S, where S is of length N corresponding to the Nunits (modules, tiles, or crystals) undergoing TOF calibration. FIG. 5diagrammatically represents Equation (4). For the d^(th)positron-electron annihilation event, Equation (4) can be written as:

Δt _(d) =c _(d,i) s _(i) +c _(d,j) s _(j)  (5)

where c_(d,i)=1 and c_(d,j)=1 (thus encoding the detectors information)and all other elements of the d^(th) row of relational matrix C havezero values. Because M>N, and more typically M>>N, it follows that theset of equations represented by matrix Equation (4) is over-determined,and can be solved in a least-squares optimization sense to determine theN elements of the skew vector S, which are then the TOF corrections forthe N detector units. Leveraging the matrix formalism, the solution canbe written as:

S=C ⁻¹ Δt   (6)

where C⁻¹ is the pseudo-inverse of the (non-square) relational matrix CAs the relational matrix C has dimensions M×N, its pseudo-inverse C⁻¹has dimensions N×M. Various approaches can be used to obtain thesolution of Equation (6)—one suitable approach is to employ singularvalue decomposition (SVD), which is a standard function in matrixprocessing libraries such as those of Matlab® (available from MathWorks,Inc., Natick, Mass., USA). The output is the optimized skew vector 92whose elements identify the TOF corrections for the N units of interest(e.g. modules, tiles, or crystals). While Expressions (4)-(6) employ amatrix formalism, more generally any approach for solving anover-determined set of equations can be employed.

With reference back to FIG. 1, the time correction module 30 applies theTOF correction values generated by the TOF calibration module 50 asfollows. Consider a list mode datum having time stamp TS (either with orwithout the Δt_(m→1) adjustment of Expression (3)) and acquired by adetector element e. The appropriate unit definitions (module definitions52, tile definitions 54, or crystal definitions 56) is referenced todetermine the corresponding detector unit (denoted here without loss ofgenerality by detector unit index i), and the time stamp TS is correctedby TS+s_(i) where the vector element s_(i) is from the TOF correctionfor detector unit i obtained from the optimized skew vector S outputfrom Expression (6).

It is to be understood that the mathematical formalism of the TOFcalibration approach described herein with reference to FIGS. 4 and 5and Expressions (4)-(6) can be modified in diverse ways without changingits underlying nature. For example, the various vectors and matrices canbe variously transposed while still producing equivalent results. Ingeneral, the calibration performed by the TOF calibration module 50entails: (1) collecting a data set of positron-electron annihilationevents where each annihilation event datum includes an identification ofthe two detector elements that detected the annihilation event and theTOF difference Δt between the 511 keV gamma ray detection events at thetwo detector elements; (2) allocating the detector elements to theirrespective detector units (e.g. modules, tiles, crystals); (3) encodingthe detector units of the annihilation events using a relational matrixC; and (4) solving an over-determined system of equations of the formΔt=CS to obtain TOF corrections represented by S, where Δt stores theannihilation event time differences Δt. In some illustrative embodimentsthe operation (4) entails computing a pseudo-inverse C⁻¹ of therelational matrix C and employing a solution of the form S=C⁻¹ Δt.However, other approaches are contemplated, such as applyingLevenberg-Marquardt least squares optimization to optimize parameters Sof the over-determined system of equations represented by Δt=CS.

With continuing reference to FIG. 5 and with further reference to FIG.6, in embodiments in which TOF corrections are to be applied at multipledetector unit levels, e.g. module, tile, and crystal levels, a suitableapproach is to apply the process of FIG. 5 in a “top-down” fashion foreach detector unit level starting at the largest unit and working downto the smallest detector unit. This approach leverages the expectationthat the TOF offsets introduced by larger detector units are likely tobe larger than the TOF offsets introduced by smaller level units. FIG. 6provides an illustrative example for the PET detector ring describedherein in which the radiation detector elements 14 are arranged intomodules, tiles (within the modules), and crystals (within the tiles). Inan operation 100, the acquired positron-electron annihilation eventsdata output by FIG. 4 operation 82 are processed at the module level inaccord with FIG. 4 operations 84, 90 to generate module-level TOFcorrections 102. In an operation 104, the module-level TOF corrections102 are applied to the calibration data so that the data are correctedfor TOF offsets introduced at the module level. Then, in an operation110, the positron-electron annihilation events data with themodule-level TOF corrections applied are processed at the tile level,again in accord with FIG. 4 operations 84, 90, to generate tile-levelTOF corrections 112. In an operation 114, the tile-level TOF corrections112 are additionally applied to the calibration data so that the dataare corrected for TOF offsets introduced at both the module and tilelevels. Finally, in an operation 120, the positron-electron annihilationevents data with the module- and tile-level TOF corrections applied areprocessed at the crystal level, again in accord with FIG. 4 operations84, 90, to generate crystal-level TOF corrections 122. During thesubsequent processing of imaging data (not shown in FIG. 6), themodule-, tile-, and crystal-level corrections 102, 112, 122 are appliedto the list mode imaging data (or, alternatively, these corrections canbe combined off-line to create a combined module+tile+crystal TOFcorrection for each detector element and the combined TOF correctionthen applied to correct the list mode imaging data). These correctionsare applied by the time correction module 30 of FIG. 1, after which the511 keV pair detector 32 is applied to identify 511 keV gamma ray pairscorresponding to positron-electron annihilation events, and TOFlocalization and image reconstruction is performed as described withreference to FIG. 1.

The invention has been described with reference to the preferredembodiments. Modifications and alterations may occur to others uponreading and understanding the preceding detailed description. It isintended that the invention be construed as including all suchmodifications and alterations insofar as they come within the scope ofthe appended claims or the equivalents thereof.

1. A time-of-flight positron emission tomography (TOF PET) imagingsystem comprising: a TOF PET scanner comprising radiation detectorelements; and an electronic data processing device programmed to:operate the TOF PET scanner to acquire calibration data comprisingannihilation event data acquired for positron-electron annihilationevents occurring in a point source located at an isocenter of the TOFPET scanner wherein each annihilation event datum includes anidentification of the radiation detector elements detecting twooppositely directed 511 keV gamma rays emitted by the annihilation eventand a time difference between detection of the two oppositely directed511 keV gamma rays emitted by the annihilation event, generate TOFcorrections for the radiation detector elements by solving anover-determined set of equations defined by the calibration data,operate the TOF PET scanner to acquire list mode imaging data comprising511 keV gamma ray detection events acquired from an imaging subject,generate corrected list mode imaging data by applying the TOFcorrections to the list mode imaging data, and reconstruct the correctedlist mode imaging data to generate a reconstructed image of at least aportion of the imaging subject.
 2. The TOF PET imaging system of claim 1wherein the electronic data processing device is programmed to generatethe TOF corrections for the radiation detector elements by operationsincluding: solving an over-determined set of equations corresponding topositron-electron annihilation events of the calibration data, theequations relating time differences of the positron-electronannihilation events with the TOF corrections for the radiation detectorelements, wherein the number of equations is greater than the number ofTOF corrections.
 3. The TOF PET imaging system of claim 1 wherein theelectronic data processing device is programmed to generate the TOFcorrections for the radiation detector elements by operations including:solving the matrix equation Δt=CS for S, where Δt stores the timedifferences of the calibration data, C is a relational matrix encodingthe identifications of the radiation detector elements, and S stores theTOF corrections.
 4. The TOF PET imaging system of claim 3 wherein thesolving comprises computing a pseudo-inverse C⁻¹ of the relationalmatrix C and computing S=C⁻¹ Δt.
 5. The TOF PET imaging system of claim3 wherein the solving comprises computing a pseudo-inverse C⁻¹ of therelational matrix C using singular value decomposition (SVD) andcomputing S=C⁻¹ Δt.
 6. The TOF PET imaging system of claim 3 wherein theelectronic data processing device is programmed to generate TOFcorrections for the radiation detector elements by operations including:grouping the radiation detector elements into detector units based ondetector unit definitions that assign radiation detector elements todetector units and constructing the relational matrix C to encode theidentifications of the radiation detector elements by detector unit; andsolving the over-determined set of equations Δt=CS for S, wherein Sstores the TOF corrections for the detector units.
 7. The TOF PETimaging system of claim 6 wherein the detector unit definitions includeat least one of: (i) detector module definitions, (ii) detector tiledefinitions wherein a detector tile is a component of a detector module,and (iii) scintillator crystal definitions wherein each detector tileincludes one or more scintillator crystals.
 8. The TOF PET imagingsystem of claim 7 wherein the electronic data processing device isprogrammed to: perform the grouping and solving operations using thedetector module definitions to generate module-level TOF corrections;apply the module-level TOF corrections to the calibration data togenerate module TOF-corrected calibration data; and perform the groupingand solving operations using detector tile definitions operating on themodule TOF-corrected calibration data to generate tile-level TOFcorrections; apply the tile-level TOF corrections to the moduleTOF-corrected calibration data to generate module and tile TOF-correctedcalibration data; and perform the grouping and solving operations forscintillator crystal definitions operating on the module and tileTOF-corrected calibration data to generate scintillator crystal-levelTOF corrections.
 9. The TOF PET imaging system of claim 1 wherein theelectronic data processing device is programmed to operate the TOF PETscanner to acquire list mode imaging data using multi-photon triggeringand is further programmed to: adjust time-stamps of the list modeimaging data to values that would have been obtained using first-photontriggering.
 10. The TOF PET imaging system of claim 1 wherein theelectronic data processing device is programmed to adjust time-stampsTS_(m) of the list mode imaging data acquired using multi-photontriggering to estimated first-photon triggered time stamps TS₁ accordingto: ${TS}_{1} = {{TS}_{m} - {a\sqrt{\frac{b}{Pm}}}}$ where a and b areconstants and Pm is the photon count for a list mode imaging datumacquired using multi-photon triggering.
 11. A non-transitory storagemedium storing instructions readable and executable by an electronicdata processing device 4 to perform a method operating on radiationdetection event data acquired using a radiation detector elementcomprising a scintillator and a light detector coupled with thescintillator, the method comprising: determining an average photon countP1 for the radiation detector element operating with first photontriggering based on calibration data acquired by the radiation detectorelement using first-photon triggering; determining a photon count Pm foran imaging radiation detection event detected by the radiation detectorelement during imaging of a subject using multi-photon triggering; andestimating a first-photon triggered time-stamp for the imaging radiationdetection event based on the values of P1 and Pm.
 12. The non-transitorystorage medium of claim 11 wherein the estimating of the first-photontriggered time stamp is based on the value √{square root over (P1/Pm)}.13. The non-transitory storage medium of claim 12 wherein the estimatingof the first-photon triggered time stamp comprises computing:${TS}_{1} = {{TS}_{m} - {a\sqrt{\frac{b}{Pm}}}}$ where TS_(m) is thetimestamp of the imaging radiation detection event using multi-photontriggering, a is a constant, and TS₁ is the estimated first-photontriggered time stamp.
 14. The non-transitory storage medium of claim 11wherein the operation of determining an average photon count P1 for theradiation detector element operating with first photon triggeringcomprises: determining P1 by fitting a Gaussian distribution to a photoncount per event histogram acquired by the radiation detector elementusing first-photon triggering.
 15. The non-transitory storage medium ofclaim 11 wherein the imaging radiation detection event is an imaging 511keV gamma ray detection event and the calibration data acquired by theradiation detector element using first-photon triggering are calibrationdata acquired by the radiation detector element for 511 keV gamma rayemissions using first-photon triggering.
 16. A method comprising:generating time of flight (TOF) corrections for radiation detectorelements of a time of flight positron emission tomography (TOF PET)scanner by solving an over-determined set of equations defined bycalibration data acquired by the TOF PET scanner from a point sourcelocated at an isocenter of the TOF PET scanner; and correcting timestamps of imaging data acquired by the TOF PET scanner from an imagingsubject using the generated TOF corrections; wherein the generating andcorrecting operations are performed by an electronic data processingdevice.
 17. The method of claim 16 wherein the calibration datacomprises 511 keV gamma ray detection events each associated with aradiation detector element of the TOF PET scanner, and the generatingoperation includes: performing time windowing on the 511 keV gamma raydetection events to identify 511 keV gamma ray detection event pairscorresponding to positron-electron annihilation events; and solving theover-determined set of equations Δt_(d)=s_(i)+s_(j) where d indexes thed^(th) 511 keV gamma ray detection event pair, i and j index the tworadiation detector elements that detected the d^(th) 511 keV gamma raydetection event pair, Δt_(d) denotes the time difference between thegamma ray detections of the 511 keV gamma ray detection event pair,s_(i) denotes the TOF correction for the i^(th) radiation detectorelement, and s_(j) denotes the TOF correction for the j^(th) radiationdetector element.
 18. The method of claim 17 wherein the generatingoperation includes: representing the over-determined set of equationsΔt_(d)=s_(i)+s_(j) by the matrix equation Δt=CS where Δt represents theTOF time differences of the 511 keV gamma ray detection event pairs, Cis a relational matrix encoding the radiation detector elements thatdetected each 511 keV gamma ray detection event pair, and S representsthe TOF corrections; and solving the matrix equation Δt=CS for S togenerate the TOF corrections.
 19. The method of claim 18 wherein thesolving comprises computing a pseudo-inverse C⁻¹ of the relationalmatrix C and computing S=C⁻¹ Δt.
 20. The method of claim 18 wherein thesolving comprises computing a pseudo-inverse C⁻¹ of the relationalmatrix C using singular value decomposition (SVD) and computing S=C⁻¹Δt.
 21. The method of claim 16 wherein the generating comprises:grouping the calibration data by detector unit based on detector unitdefinitions that assign radiation detector elements of the TOF PETscanner to detector units; and solving the over-determined set ofequations defined by the calibration data with the radiation detectorelements identified in the calibration data by detector unit based onthe grouping so as to generate TOF corrections for the detector units.22. The method of claim 21 wherein the detector unit definitions assignradiation detector elements of the TOF PET scanner to at least one of:(i) detector modules, (ii) detector tiles within detector modules, and(iii) scintillator crystals within detector tiles.
 23. The method ofclaim 22 wherein the generating comprises repeating the grouping andsolving for detector modules, detector tiles, and scintillator crystalsin succession with each successive repetition acting on the calibrationdata corrected by the TOF corrections generated by the previousrepetition.
 24. The method of claim 16 further comprising: adjusting atime stamp of a 511 keV gamma ray detection event of the imaging dataacquired by a radiation detector element using multi-photon triggeringto an adjusted time stamp corresponding to first-photon triggering basedon the value √{square root over (P1/Pm)} where P1 is an average 511 keVgamma ray detection photon count for the radiation detector elementusing first-photon triggering and Pm is the photon count of the 511 keVgamma ray detection event of the imaging data.
 25. The method of claim16 wherein the calibration data comprises 511 keV gamma ray detectionevents each associated with a radiation detector element of the TOF PETscanner, and the generating operation includes: performing timewindowing on the 511 keV gamma ray detection events to identify 511 keVgamma ray detection event pairs corresponding to positron-electronannihilation events; and solving the over-determined set of equationscorresponding to the positron-electron annihilation events, theequations relating time differences of the positron-electronannihilation events with the TOF corrections for the radiation detectorelements, wherein the set of equations is over-determined because thenumber of equations is greater than the number of TOF corrections.